Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Select the correct answer.

What is the equation of the line that has a slope of 3 and goes through the point [tex]$(-3,-5)$[/tex]?

A. [tex]$y = 3x + 4$[/tex]
B. [tex]$y = 3x - 14$[/tex]
C. [tex]$y = 3x - 4$[/tex]
D. [tex]$y = 3x + 12$[/tex]

Sagot :

GinnyAnswer
To find the equation of a line given a point on the line and the slope, we use the slope-intercept form of the equation of a line, which is:

[tex]\[ y = mx + b \][/tex]

where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

Given:
- The slope [tex]\( m = 3 \)[/tex]
- A point [tex]\( (-3, -5) \)[/tex] that lies on the line

We need to find the y-intercept [tex]\( b \)[/tex]. To do this, we substitute the given point [tex]\( (x, y) \)[/tex] into the equation:

[tex]\[ y = mx + b \][/tex]

Plugging in the values, we get:

[tex]\[ -5 = 3(-3) + b \][/tex]

Now solve for [tex]\( b \)[/tex]:

[tex]\[ -5 = -9 + b \][/tex]

Add 9 to both sides:

[tex]\[ -5 + 9 = b \][/tex]

[tex]\[ b = 4 \][/tex]

So the y-intercept [tex]\( b \)[/tex] is 4. Therefore, the equation of the line is:

[tex]\[ y = 3x + 4 \][/tex]

Thus, the correct answer is:

A. [tex]\( y = 3x + 4 \)[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.